Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Sparse reconstruction of guided wavefield from limited measurements using compressed sensing

  • Qiao, Baijie (The State Key Laboratory for Manufacturing Systems Engineering) ;
  • Mao, Zhu (Department of Mechanical Engineering, University of Massachusetts Lowell) ;
  • Sun, Hao (Department of Civil Engineering, Northeastern University) ;
  • Chen, Songmao (Department of Mechanical Engineering, University of Massachusetts Lowell) ;
  • Chen, Xuefeng (The State Key Laboratory for Manufacturing Systems Engineering)
  • Received : 2019.04.18
  • Accepted : 2019.07.12
  • Published : 2020.03.25
⟨ Previous Next ⟩

Abstract

A wavefield sparse reconstruction technique based on compressed sensing is developed in this work to dramatically reduce the number of measurements. Firstly, a severely underdetermined representation of guided wavefield at a snapshot is established in the spatial domain. Secondly, an optimal compressed sensing model of guided wavefield sparse reconstruction is established based on l1-norm penalty, where a suite of discrete cosine functions is selected as the dictionary to promote the sparsity. The regular, random and jittered undersampling schemes are compared and selected as the undersampling matrix of compressed sensing. Thirdly, a gradient projection method is employed to solve the compressed sensing model of wavefield sparse reconstruction from highly incomplete measurements. Finally, experiments with different excitation frequencies are conducted on an aluminum plate to verify the effectiveness of the proposed sparse reconstruction method, where a scanning laser Doppler vibrometer as the true benchmark is used to measure the original wavefield in a given inspection region. Experiments demonstrate that the missing wavefield data can be accurately reconstructed from less than 12% of the original measurements; The reconstruction accuracy of the jittered undersampling scheme is slightly higher than that of the random undersampling scheme in high probability, but the regular undersampling scheme fails to reconstruct the wavefield image; A quantified mapping relationship between the sparsity ratio and the recovery error over a special interval is established with respect to statistical modeling and analysis.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, China Postdoctoral Science Foundation

The first author would like to acknowledge the support from the National Natural Science Foundation of China (No. 51705397) and China Postdoctoral Science Foundation (No. 2019T120900 & 2017M610636). The primary part of the presented work was completed during the first author's visit to the Structural Dynamics and Acoustic Systems Laboratory at the University of Massachusetts Lowell.

References

  1. Alguri, K.S. and Harley, J.B. (2016), "Consolidating guided wave simulations and experimental data: a dictionary learning approach", Proceedings of SPIE Smart Structures and Materials, Nondestructive Evaluation and Health Monitoring, 98050Y-98050Y-10. https://doi.org/10.1117/12.2219420
  2. Beck, A. and Teboulle, M. (2009), "A fast iterative shrinkagethresholding algorithm for linear inverse problems", SIAM J. Imaging Sci., 2(1), 183-202. https://doi.org/10.1137/080716542
  3. Bioucas-Dias, J.M. and Figueiredo, M.A.T. (2007), "A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration", IEEE Transact. Image Process., 16(12), 2992-3004. https://doi.org/10.1109/TIP.2007.909319
  4. Candes, E. and Romberg, J. (2007), "Sparsity and incoherence in compressive sampling", Inverse Probl., 23(3), 969. https://doi.org/10.1088/0266-5611/23/3/008
  5. Candes, E.J. and Wakin, M.B. (2008), "An introduction to compressive sampling", IEEE Signal Process. Mag., 25(2), 21-30. https://doi.org/10.1109/MSP.2007.914731
  6. Chen, D.M., Xu, Y.F. and Zhu, W.D. (2018a), "Identification of damage in plates using full-field measurement with a continuously scanning laser Doppler vibrometer system", J. Sound Vib., 422, 542-567. https://doi.org/10.1016/j.jsv.2018.01.005
  7. Chen, Y., Joffre, Y.D. and Avitabile, P. (2018b), "Underwater dynamic response at limited points expanded to full-field strain response", J. Vib. Acoust., 140(5), 051016. https://doi.org/10.1115/1.4039800
  8. Di Ianni, T., De Marchi, L., Perelli, A. and Marzani, A. (2015), "Compressive sensing of full wave field data for structural health monitoring applications", IEEE Transact. Ultrason. Ferr. Freq. Control, 62(7), 1373-1383. https://doi.org/10.1109/TUFFC.2014.006925
  9. Donoho, D. (2006), "Compressed sensing", IEEE Transact. Inform. Theory, 52(4), 1289-1306. https://doi.org/10.1109/TIT.2006.871582
  10. Duarte, M.F., Davenport, M.A., Takhar, D., Laska, J.N. and Sun, T. (2008), "Single-pixel imaging via compressive sampling", IEEE Signal Process. Mag., 25(2), 83-91. https://doi.org/10.1109/MSP.2007.914730
  11. Figueiredo, M.A.T., Nowak, R.D. and Wright, S.J. (2007), "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems", IEEE J. Select. Topics Signal Process., 1(4), 586-597. https://doi.org/10.1109/JSTSP.2007.910281
  12. Flynn, E.B. and Jarmer, G.J. (2013), "High-speed, non-contact, baseline-free imaging of hiddden defects using scanning laser measurements of steady state ultrasonic vibration", Struct. Health Monit., 1, 1186-1193.
  13. Ginsberg, D., Fritzen, C.P. and Loffeld, O. (2018), "Sparsityconstrained extended Kalman filter concept for damage localization and identification in mechanical structures", Smart Struct. Syst., Int. J., 21(6), 741-749. https://doi.org/10.12989/sss.2018.21.6.741
  14. Harley, J.B. (2016), "Predictive guided wave models through sparse modal representations", Proceedings of the IEEE, 104(8), 1604-1619. https://doi.org/10.1109/JPROC.2015.2481438
  15. Hennenfent, G. and Herrmann, F.J. (2008), "Simply denoise: wavefield reconstruction via jittered undersampling", Geophysics, 73(3), 19-28. https://doi.org/10.1190/1.2841038
  16. Herrmann, F., Friedlander, M. and Yilmaz, O. (2012), "Fighting the curse of dimensionality: Compressive sensing in exploration seismology", IEEE Signal Process. Mag., 29(3), 88-100. 10.1109/MSP.2012.2185859
  17. Hong, M., Mao, Z., Todd, M.D. and Su, Z. (2017), "Uncertainty quantification for acoustic nonlinearity parameter in Lamb wavebased prediction of barely visible impact damage in composites", Mech. Syst. Signal Process., 82, 448-460. https://doi.org/10.1016/j.ymssp.2016.05.035
  18. Kim, S.J., Koh, K., Lustig, M., Boyd, S. and Gorinevsky, D. (2007), "An interior-point method for large-scale l1-regularized least squares", IEEE J. Select. Topics Signal Process., 1(4), 606-617. https://doi.org/10.1109/JSTSP.2007.910971
  19. Kirkup, L. and Frenkel, R.B. (2006), An Introduction to Uncertainty in Measurement: using the GUM (guide to the expression of uncertainty in measurement), Cambridge University Press.
  20. Lu, Y., Ye, L., Wang, D., Zhou, L. and Cheng, L. (2010), "Piezoactivated guided wave propagation and interaction with damage in tubular structures", Smart Struct. Syst., Int. J., 6(7), 835-849. https://doi.org/10.12989/sss.2010.6.7.835
  21. Mesnil, O. and Ruzzene, M. (2016), "Sparse wavefield reconstruction and source detection using compressed sensing", Ultrasonics, 67, 94-104. https://doi.org/10.1016/j.ultras.2015.12.014
  22. Montgomery, D.C., Runger, G.C. and Hubele, N.F. (2010), Engineering Statistics, (5th Edition), John Wiley & Sons.
  23. Park, H.J., Sohn H., Yun, C.B., Chung, J. and Kwon, I. (2010), "A wireless guided wave excitation technique based on laser and optoelectronics", Smart Struct. Syst., Int. J., 6(5-6), 749-765. https://doi.org/10.12989/sss.2010.6.5_6.749
  24. Park, B., An, Y.K. and Sohn, H. (2014), "Visualization of hidden delamination and debonding in composites through noncontact laser ultrasonic scanning", Compos. Sci. Technol., 100, 10-18. https://doi.org/10.1016/j.compscitech.2014.05.029
  25. Perelli, A., Di Ianni, T., Marzani, A., De Marchi, L. and Masetti, G. (2013), "Model-based compressive sensing for damage localization in Lamb wave inspection", IEEE Transact. Ultrason. Ferr. Freq. Control, 60(10), 2089-2097. 10.1109/TUFFC.2013.2799
  26. Qiao, B., Chen, X., Luo, X. and Xue, X. (2015), "A novel method for force identification based on the discrete cosine transform", J. Vib. Acoust., 137(5), 051012. https://doi.org/10.1115/1.4030616
  27. Qiao, B., Zhang, X., Gao, J., Liu, R. and Chen, X. (2016a), "Impact-force sparse reconstruction from highly incomplete and inaccurate measurements", J. Sound Vib., 376, 72-94. https://doi.org/10.1016/j.jsv.2016.04.040
  28. Qiao, B., Zhang, X., Wang, C., Zhang, H. and Chen, X. (2016b), "Sparse regularization for force identification using dictionaries", J. Sound Vib., 368, 71-86. https://doi.org/10.1016/j.jsv.2016.01.030
  29. Qiao, B., Zhu, M., Liu, J., Zhao, Z. and Chen, X. (2019), "Group sparse regularization for impact force identification in time domain", J. Sound Vib., 445, 44-63. https://doi.org/10.1016/j.jsv.2019.01.004
  30. Sohn, H., Dutta, D., Yang, J.Y., DeSimio, M., Olson, S. and Swenson, E. (2011), "Delamination detection in composites through guided wave field image processing", Compos. Sci. Technol., 71(9), 1250-1256. https://doi.org/10.1016/j.compscitech.2011.04.011
  31. Song, W., Xiang, J. and Zhong, Y. (2017), "Mechanical parameters detection in stepped shafts using the FEM based IET", Smart Struct. Syst., Int. J., 20(4), 473-481. https://doi.org/10.12989/sss.2017.20.4.473
  32. Staszewski, W., Lee, B., Mallet, L. and Scarpa, F. (2004), "Structural health monitoring using scanning vibrometry: I. Lamb wave sensing", Smart Mater. Struct., 13(2), 251-260. https://doi.org/10.1088/0964-1726/13/2/002
  33. Su, Z., Ye, L. and Lu, Y. (2006), "Guided Lamb waves for identification of damage in composite structures: A review", J. Sound Vib., 295(3-5), 753-780. https://doi.org/10.1016/j.jsv.2006.01.020
  34. Tropp, J. and Wright, S.J. (2010), "Computational methods for sparse solution of linear inverse problems", P. IEEE, 98(6), 948-958. 10.1109/JPROC.2010.2044010
  35. Wright, S.J., Nowak, R.D. and Figueiredo, M.A.T. (2009), "Sparse reconstruction by separable approximation", IEEE Transact. Signal Process., 57(7), 2479-2493. https://doi.org/10.1109/TSP.2009.2016892
  36. Xiang, J., Matsumoto, T., Long, J. Wang, Y. and Jiang, Z. (2012), "A simple method to detect cracks in beam-like structures", Smart Struct. Syst., Int. J., 9(4), 335-353. https://doi.org/10.12989/sss.2012.9.4.335
  37. Xiang, J., Nackenhorst, U., Wang, Y., Jiang, Y., Gao, H. and He, Y. (2014), "A new method to detect cracks in plate-like structures with though-thickness cracks", Smart Struct. Syst., Int. J., 14(3), 397-418. https://doi.org/10.12989/sss.2014.14.3.397
  38. Xu, C., Yang, Z., Chen, X., Tian, S. and Xie, Y. (2018), "A guided wave dispersion compensation method based on compressed sensing", Mech. Syst. Signal Process., 103, 89-104. https://doi.org/10.1016/j.ymssp.2017.09.043
  39. Yang, Z.B., Radzienski, M., Kudela, P. and Ostachowicz, W. (2017), "Damage detection in beam-like composite structures via Chebyshev pseudo spectral modal curvature", Compos. Struct., 168, 1-12. https://doi.org/10.1016/j.compstruct.2017.01.087
  40. Yang, Z., Yu J., Tian, S., Chen, X. and Xu, G. (2018), "A damage localization method based on the singular value decomposition (SVD) for plates", Smart Struct. Syst., Int. J., 22(5), 621-630. https://doi.org/10.12989/sss.2018.22.5.621
  41. Yang, Z.B., Wang, Z.K., Tian, S.H. and Chen, X.F. (2019), "Analysis and modelling of non-Fourier heat behavior using the wavelet finite element method", Materials, 12(8), 1337. https://doi.org/10.3390/ma12081337